Subgroups — C₂²×#14583836 #26012565

Order 11072.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583836	C₂	1	12	yes	maximal, direct product factor
2	C₂²×#13063443	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₁₇₃	C₂	1	1	yes	maximal, characteristic
4	#14583836	C₂²	1	16	yes	direct product factor
5	C₂×#13063443	C₂²	1	12	yes	complemented
6	C₂³×D₁₇₃	C₄	1	1	yes	characteristic
7	C₂²×Dic₁₇₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₁₇₃	C₄	1	6	yes	—
9	C₂×C₄×D₁₇₃	C₂²	1	6	yes	—
10	C₂²×C₄×C₁₇₃	C₄	1	1	yes	characteristic
11	#13063443	C₂³	1	8	yes	complemented
12	C₂²×D₁₇₃	—	2	4	no	—
13	C₂²×D₁₇₃	C₂×C₄	1	6	yes	—
14	C₂×Dic₁₇₃	C₂×C₄	1	3	yes	—
15	C₂×Dic₁₇₃	C₂³	1	3	yes	—
16	C₄×D₁₇₃	C₂×C₄	1	12	yes	—
17	C₄×D₁₇₃	C₂³	1	4	yes	—
18	C₂³×C₁₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₇₃	C₂×C₄	1	6	yes	—
20	C₂²×C₁₇₃	M₁₆	1	4	yes	complemented
21	C₂²×C₁₇₃	C₂²×C₄	1	3	yes	—
22	C₂×D₁₇₃	—	2	12	no	—
23	C₂×D₁₇₃	C₂²×C₄	1	4	yes	—
24	C₄×C₁₇₃	C₂²×C₄	1	4	yes	—
25	Dic₁₇₃	C₂²×C₄	1	3	yes	—
26	Dic₁₇₃	C₂⁴	1	1	yes	characteristic
27	C₂×C₁₇₃	C₂×M₁₆	1	6	yes	complemented
28	C₂×C₁₇₃	C₂³×C₄	1	1	yes	characteristic
29	D₁₇₃	—	2	4	no	—
30	C₁₇₃	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂²×M₁₆	—	173	1	no	maximal, Sylow
32	C₂³×C₄	—	173	1	no	—
33	C₂×M₁₆	—	173	12	no	—
34	C₂²×C₈	—	173	2	no	—
35	C₂⁴	—	173	1	no	—
36	C₂²×C₄	—	173	1	no	—
37	C₂²×C₄	—	173	6	no	—
38	C₂²×C₄	—	173	6	no	—
39	C₂²×C₄	#10621924	1	1	yes	characteristic
40	M₁₆	—	173	16	no	—
41	C₂×C₈	—	173	12	no	—
42	C₂³	—	346	4	no	—
43	C₂³	—	173	6	no	—
44	C₂³	C₂×#10621924	1	1	yes	characteristic
45	C₂×C₄	—	173	3	no	—
46	C₂×C₄	—	173	3	no	—
47	C₂×C₄	—	173	12	no	—
48	C₂×C₄	—	173	4	no	—
49	C₂×C₄	C₂×#10621924	1	6	yes	—
50	C₈	—	173	8	no	—
51	C₂²	—	346	12	no	—
52	C₂²	—	173	4	no	—
53	C₂²	#14583836	1	4	yes	direct product factor
54	C₂²	C₂²×#10621924	1	3	yes	—
55	C₄	—	173	1	no	—
56	C₄	—	173	3	no	—
57	C₄	C₂²×#10621924	1	4	yes	—
58	C₂	—	346	4	no	—
59	C₂	C₂×#14583836	1	6	yes	direct product factor
60	C₂	C₂³×#10621924	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#10621924
commutator	C₂×C₁₇₃	C₂³×C₄
Frattini	C₂	C₂³×#10621924
Fitting	C₂²×C₄×C₁₇₃	C₄
socle	C₂³×C₁₇₃	C₂×C₄
prime radical	C₂³×D₁₇₃	C₄
cosocle	Dic₁₇₃	C₂⁴
hypercenter	C₂²×C₄	#10621924
hypocenter	C₁₇₃	C₂²×M₁₆
LCS	G ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#14583836	C₂	direct (N × H)
2. C₂²×#13063443	C₂	semidirect
4. #14583836	C₂²	direct (N × H)
5. C₂×#13063443	C₂²	semidirect
11. #13063443	C₂³	semidirect
20. C₂²×C₁₇₃	M₁₆	semidirect
27. C₂×C₁₇₃	C₂×M₁₆	semidirect
30. C₁₇₃	C₂²×M₁₆	semidirect
53. C₂²	#14583836	direct (N × H)
59. C₂	C₂×#14583836	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#14583836	2
C₂²×#13063443	2
C₂²×C₄×D₁₇₃	2
C₂²×M₁₆	173

Subgroups — C22×#14583836 #26012565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#14583836 #26012565